loading page

A class of multiparameter p-Laplacian elliptic systems in the exterior of a ball
  • Meiqiang Feng,
  • Yichen Zhang
Meiqiang Feng
Beijing Information Science and Technology University
Author Profile
Yichen Zhang
Beijing Information Science and Technology University
Author Profile

Abstract

We prove the existence, multiplicity and nonexistence of positive radial solutions to the following p-Laplacian equations $$ \left \{ \begin{array}{l} -\triangle_p z_1=g_1(|x|,z_1,z_2,a,b) \ \ \text{in} \ \Omega,\\ -\triangle_p z_2=g_2(|x|,z_1,z_2,a,b) \ \ \text{in} \ \Omega,\\ (z_1, z_2) \rightarrow (0,0)\ \ as\ \ |x|\rightarrow \infty,\\ \frac{\partial z_1}{\partial n} =\frac{\partial z_2}{\partial n}= 0\ \ \text{on}\ \ |x|=r_0, \end{array} \right. $$ where $\triangle_p u=\text{div}({|\nabla u|}^{p-2}\nabla u),\ 1r_0>0\}$.